Journal of Health & Medical Economics

Introduction

Econometric models have played a role in assessing the forces that increase in the demand for medical care.Numerous economy-based studies have investigated the demand for medical care. Duan et al. [1] studied the decision-making behaviors of patients. In the first stage, patients consider visiting a physician. On visiting, physicians determine the treatment intensity which influences the medical care expenditure. Therefore, considering visiting a physician, the number of physician visits, and medical care expenditure are the commonly studied variables that represent the demand for medical care. Among these variables, medical care expenditure is the most likely to increase with increase in the number of physician visits. In the next, we briefly introduce some econometric models that fit the features of medical data.

Econometric models

A physician visit is a dichotomous dependent variable. For modeling the likelihood of visiting a physician, probit and logit models can be used for cross-sectional data, whereas Chamberlain's[2] fixed-effect logit model can be used for panel data. The fixed-effect logit model can reduce the problems of unobserved heterogeneity and omitted variable bias, both of which invalidate cross-sectional data analyses. Count data models, such as the Poisson and negative binomial models, have been proposed for studying the number of physician visits; the Poisson model assumes equality between the mean and variance whereas the negative binomial model does not. However, the ability of these models to deal with zero values is quite limited because it depends on their mean and variance. In case of excessive zero values, alternative models, such as zero-inflated Poisson and zero-inflated negative binomial models, are used. Among these four models, the zero-inflated negative binomial model is the most generalized because it can counter the problems caused by excessive zero values and over-dispersion.

The zero-inflated models separate the zeros into two exclusive and independent groups, members of one group never visit physicians, whereas those of the other group do. In other words, the zero-inflated models assume that some fraction of the zero-sample is likely to permanently avoid visiting physicians. This statistical technique is widely used in microeconometrics. Schmidt and Witte [3] proposed a “split population model,” in which some fraction of the sample is assumed to never return to prison. Hsiao and Sun [4] proposed a “one-sided survey response bias model,” in which the response is biased only in one direction. While utilizing the zero-inflated models, the assumption that some people avoid visiting physicians must be justified.

In addition tothe numerous zero values, analyzing medical care expenditure is complex because of logarithmic transformation of the non-zero data can reduce this selection bias arises when health plan enrollees can choose their plan according to their health conditions. For example, using a data set from the 1994 Medicare Current Beneficiary Survey, Riley et al. [5] reported that medicare beneficiaries enrolled in Health Maintenance Organization (HMO) are mostly healthier than those in Fee For Service (FFS). This implies that the choice between HMO and FFS depends on non-random sampling.

selection biassample selection models with a bivariate normal distribution [6] and two-part models [1,7] have been suggested. In the first part of the two-part model, a probit model is used to manage the dichotomous outcomes of an individual’s visit to the physician and to predict the probability of the individual visiting a physician. In the second part, the level of medical care expenditure is determined using only those observations with non-zero values. By contrast, the sample selection model considers observations with zero values. Whether to use two-part models or sample selection models is highly debated [8,9]. Using Monte Carlo methods, Leung and Yu [9] reported that Heckman’s [10] two-step estimator for the sample selection model is vulnerable to multicollineaity. However, in empirical applications of health economics, two-part models are generally favored [11] for the prediction ability of actual outcomes. The high performance of the two-part model is attributable to the aforementioned nonuse of zero-value observations.Conversely, the high degree of censoring caused by excessive zero values may cause Heckman’s two-step estimator to violate the bivariate normality assumption. Similar to the Poisson and negative binomial models, the sample selection model may have limited ability to solve the problems caused by excessive zero values. A common approach is to use the sample selection model, in conjunction with the zero-inflated model. Recently, sample selection models for panel data, such as proposed by Kyriazidou [12], are devoid excess zeros and multicollinearity. The advantage of using the two-part model is inapplicable if empirical applications to panel data [13].

Conclusion

Estimation of a demand for medical care equations plays a vital role for public policymakers. To the best of our knowledge, the issue of excess zeros has previously been ignored in the literature on sample selection models. In this article, we argue that while using sample selection models the excessive number of zeros may lead to violations of the distributional assumption and affect their prediction. We encourage further study on modeling sample selection model to deal with excess zeros.

References

1. Duan N, Manning W, Morris C, Newhouse J (1983) A comparison of alternative models for the demand for medical care. Journal of Business & Economic Statistics 1:115-126.
2. Chamberlain G (1984) Panel data.in: Griliches Z, Intriligator M (Eds), Handbook of Econometrics, North-Holland, Amsterdam, 2: 1247-1318.
3. Schmidt P, Witte A(1989)Predicting criminal recidivism using 'split population' survival time models. Journal of Econometrics 40: 141-159.
4. Hsiao C, Sun BH, (1999) Modeling survey response bias - with an analysis of the demand for an advanced electronic device. Journal of Econometrics 89: 15-39.
5. Riley G, Tudor C, Chiang Y, Ingber M (1996) Health status of medicare enrollees in HMO’s and fee for service in 1994. Health Care Financing Review 17: 65-76.
6. Van de Ven WPMM, Gaag BV(1982) Health as an unobservable: a MIMIC - model of the demand for health care. Journal of Health Economics 1: 157-183.
7. Manning WG, Duan N, Rogers W (1987) Monte Carlo evidence on the choice between sample selection and two part models. Journal of Econometrics 35: 59-82.
8. Pohlmeier W, Ulrich V (1995)Aneconometric model of the two-part decisionmakingprocess in the demand for health care. The Journal of Human Resources 30: 339-361.
9. Leung SF, Yu S (1996)On the choice between sample selection and two-part models. Journal of Econometrics 72:197-229.
10. Heckman JJ (1979) Sample selection bias as a specification error. Econometrica 47:153-161.
11. Madden D (2008) Sample selection versus two-part models revisited: The case of female smoking and drinking. Journal of Health Economics 27: 300-307.
12. Kyriazidou E (1997) Estimation of a panel data sample selection model. Econometrica 65:1335-1364.
13. Cameron C, Trivedi P, Milne F, Piggott J (1988)Amicroeconometric model of the demand for health care and health insurance in Australia. Review of Economics Studies 55: 85-106.